shamsuzzoha_mepec 2011 conference

8/3/2019 Shamsuzzoha_MEPEC 2011 Conference

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One Step Procedure for PI/PIDController Tuning in Closed-Loop

M. Shamsuzzoha, Al-Shammari, Hiroya Sekia

Department of Chemical Engineering, King Fahd University ofPetroleum and Minerals, Daharan, Kingdom of Saudi Arabia

Email: [email protected] Resources Laboratory, Tokyo Institute of Technology,

4259-R1-19 Nagatsuta, Yokohama 226-8503, Japan

MEPEC 2011, Bahrain, 25th October 2011


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Motivation Desborough and Miller (2001): More than 97% of controllers are PID

Vast majority of the PID controllers do not use D-action.

PI controller: Only two adjustable parameters but still not easy to tune

Many industrial controllers poorly tuned

Ziegler-Nichols closed-loop method (1942) is popular, but Requires sustained oscillations

Tunings relatively poor

Big need for a fast and improved closed-loop tuning procedure


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Outline1. Existing approaches to PID tuning

2. Proposed PID tuning rules

3. Closed-loop setpoint experiment

4. Correlation between setpoint response and proposed PID-settings5. Final choice of the controller settings (detuning)

6. Analysis and Simulation

7. Conclusion


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1. Common approach:

PID-tuning based on open-loop model Step 1: Open-loop experiment: Most tuning approaches are based on open-loop plant model

gain (k), time constant () time delay ()

Problem: Loose control during identification experiment

Step 2: TuningMany approaches

IMC-PID (Rivera et al., 1986): good for setpoint change SIMC-PI (Skogestad, 2003): Improved for integrating disturbances IMC-PID (Shamsuzzoha and Lee, 2007&2009) for disturbance

rejection Shamsuzzoha and Skogestad (2010): The setpoint overshoot

method (Closed-loop tuning method)


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Alternative approach:PI-tuning based on closed-loop data

Ziegler-Nichols (1942) closed-loop methodStep 1. Closed-loop experiment

Use P-controller with sustained oscillations. Record:1. Ultimate controller gain (Ku)2. Period of oscillations (Pu)

Step 2. Simple PI rules: Kc=0.45Kuand I=0.83Pu.

Advantages ZN: Closed-loop experiment Very little information required Simple tuning rules

Disadvantages: System brought to limit of instability Relay test (strm) can avoid this problem but requires the feature of switching to

on/off-control Settings not very good: Aggressive for lag-dominant processes (Tyreus and Luyben) and

quite slow for delay-dominant process (Skogestad).

Only for processes with phase lag > -180o

(does not work on second-order)


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Want to develop improved andsimpler alternative to ZN:

Closed-loop setpointresponse with P-controller Use P-gain about 50% of

ZN Identify key parameters

from setpoint response: Simplest to observe is first

peak!

py

pt

y sy

t0t

uy

sy

y

This work.

Improved closed-loop PI-tuning method

Idea: Derive correlation between key parameters and proposedPID-settings for corresponding process


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2. Proposed PID tuning rules

ys

d

c gyu+

-

First-order process with time delay:-

( )1

skeg s

s

PID controller:

Proposed PID controller based on Direct Synthesis:

c =Fast and robust setting:

1

1c DI

c s K ss

2

2c

c

Kk

2D

I c

=min , 4( +)2c

2

3cK

k

min , 8

2I

2D


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py

pt

y

sy

t0t

uy

sy

Procedure: Switch to P-only mode and make

setpoint change Adjust controller gain to get

overshoot about 0.30 (30%)

Record key parameters:1. Controller gain Kc02. Overshoot = (yp-y)/y3. Time to reach peak (overshoot), tp4. Steady state change,b = y/ys.

Estimate of y without waiting to settle:

y = 0.45(yp+ yu)

Advantages compared to ZN:* Not at limit to instability* Works on a simple second-order process.

3. Closed-loop setpoint experiment

Closed-loop step setpoint response with P-only control.


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Various overshoots (10%-60%)

10 1

seg

s

0 5 10 15 20 25 300

0.25

0.5

0.75

1

1.25

time

OUTPUTy

Setpoint

/=1 (Kc0

=0.855)

/=0.4 (Kc0

=0.404)

/=100 (Kc0

=79.9)

/=2 (Kc0

=1.636)

/=5 (Kc0

=4.012)

/=10 (Kc0

=8.0)

/=0.2 (Kc0

= 0.309)

/=0 (Kc0

= 0.3)

Closed-loop setpoint experiment

Overshoot of 0.3 (30%) with different s

30%

=0

=100

=2

Small : Kc0 small and b small

0 5 10 15 20 250

0.25

0.5

0.75

1

1.25

1.5

time

OUTPUT

y

overshoot=0.10 (Kc0

=5.64)

overshoot=0.20 (Kc0

=6.87)

overshoot=0.30 (Kc0

=8.0)

overshoot=0.40 (Kc0

=9.1)

overshoot=0.50 (Kc0

=10.17)

overshoot=0.60 (Kc0

=11.26)

setpoint


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Estimate ofy using undershoot yu

py

pt

y sy

t0t

uy

sy

y

Line: y = 0.8947(yp+ yu)/2

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1 1,2

(yp+ yu)/2

y

overshoot=0.6

overshoot=0.5

overshoot=0.4

overshoot=0.3

overshoot=0.2

Data: 15 first-order with delay processes using 5 overshoots each (0.2, 0.3, 0.4, 0.5, 0.6). ys=1

Conclusion:

y 0.45(yp+yu)


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4. Correlation between Setpointresponse and proposed PID-settings

Goal: Find correlation between proposed PID-settings and keyparameters from 90 setpoint experiments.

Consider 15 first-order plus delay processes:/ = 0.1, 0.2, 0.4, 0.8, 1, 1.5, 2, 2.5, 3, 5, 7.5, 10, 20,

50, 100

For each of the 15 processes: Obtain proposed PID-settings (Kc,I) Generate setpoint responses with 6 different overshoots (0.10, 0.20,

0.30, 0.40, 0.50, 0.60)and record key parameters(Kc0, overshoot, tp, b)

-

( ) 1

seg s s


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Fixed overshoot:Slope Kc/Kc0 = A approx. constant,

independent of the value of /

c

c0

K=A

K

Correlation Setpoint response and proposed PID-settings

Controller gain (Kc)

Kc0

Kc

Agrees with ZN (approx. 100% overshoot):Original: Kc/Kcu = 0.45

Tyreus-Luyben: Kc/Kcu = 0.33

90 cases: Plot Kcas a function ofKc0

0 20 40 60 80 100 1200

10

20

30

40

50

60

70

kKc0

kKc

0.10 overshoot

kKc=1.1621kK

c0

0.20 overshoot

kKc=0.9701kK

c0

0.30 overshoot

kKc=0.841kK

c0

0.40 overshoot

kKc=0.7453kK

c0

0.50 overshoot

kKc=0.6701kK

c0

0.60 overshoot

kKc=0.6083kK

c0


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2A= 1.55(overshoot) - 2.159(overshoot) + 1.35 Overshoots between 0.1 and 0.6(should not be extended outside this range).

Conclusion: Kc = Kc0 A

A = slope

overshoot

0.1 0.2 0.3 0.4 0.5 0.6

0.7

0.8

0.9

1

1.1

overshoot (fractional)

A

y = 1.55*(overshoot)2 - 2.159*(overshoot) + 1.35


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I1b

=1.5A1-b

Proposed PID-rules

Case 1 (large delay): I1= +/2 Case 2 (small delay): I2 = 8

Case 1 (large delay):

= 1.5*kKc*-0.5* (substitute I = +/2 into the proposed rule for Kc)c c0 c c0 c0kK =kK K K kK A

c0

b

kK = (1-b)

Correlation Setpoint response and proposed PID-settings

Integral time (I)

(from steady-state offset)

Conclusion so far:

Still missing: Correlation for

I 1.5 ckK


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0.1 0.3 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Overshoot

/tp

0.43 (I1

)

0.305 (I2

)

/=0.1

/=8

/=100

/=1

I I1 I p2 p

b =min( , ) min 0.645A , 2.44t

1-bt

Correlation between and tp

py

pt

y sy

t0t

uy

sy

/tp

overshoot

Use:/tp= 0.43 for I1 (large delay)/tp = 0.305 for I2 (small delay)

Conclusion:

tp


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Derivative action (D)

The derivative action can increase stability and improvethe closed-loop performance.

Case I: For approximately integrating process (>>)

Case II: The processeswith a relatively large delay

Summary: The derivative action for both the cases i.e.,D1 and D2 are approximately same

0.14 1

1-D p

bt if A

b

10.305 0.15

2 2 2

p

D pt t

2 2

2

0.430.1433

2 3 3 3

p

D p

tt


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Choice of detuning factor F:

F=1. Good tradeoff between fast and robust (SIMC with c=)

F>1: Smoother control with more robustness

F


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6. Analysis: Simulation PID-control

5 1

seg

s

First-order + delay process

t=0: Setpoint change t=40: Load disturbance

in training setsimilar response as SIMC

0 20 40 60 800

0.25

0.5

0.75

1

1.25

time

OUTPUT

y

Shamsuzzoha and Skogestad method with F=1(overshoot=0.10)Shamsuzzoha and Skogestad method with F=1(overshoot=0.298)

Shamsuzzoha and Skogestad method with F=1 (overshoot=0.599)

Proposed method with F=1(overshoot=0.10)Proposed method with F=1(overshoot=0.298)

Proposed method with F=1(overshoot=0.599)


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sg e s

Integrating process

Analysis: Simulation PID-control

in training set

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

OUTPUT

y

Shamsuzzoha and Skogestad method with F=1 (overshoot=0.108)Shamsuzzoha and Skogestad method with F=1 (overshoot=0.302)

Shamsuzzoha and Skogestad method with F=1 (overshoot=0.60)Proposed method with F=1 (overshoot=0.108)

Proposed method with F=1 (overshoot=0.302)



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Responses for PI-control of second-order process g=1/(s+1)(0.2s+1).

1

1 0.2 1g

s s

Second-order process


Not in training set

0 2 4 6 8 100

0.25

0.5

0.75

1

1.25

1.5

time

OUTPUT

y








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Responses for PI-control of high-order process g=1/(s+1)(0.2s+1)(0.04s+1)(0.008s+1).

1

1 0.2 1 0.04 1 0.008 1g

s s s s

High-order process


Not in training set

0 5 10 15 200

0.25

0.5

0.75

1

1.25

time

OUTPUT

y



Shamsuzzoha and Skogestad method with F=1(overshoot=0.598)Proposed method with F=1(overshoot=0.104)




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2

1

1g

s s

Third-order integrating

process


Not in training set

0 40 80 120 160 2000

1

2

3

4

5

time

OUTPUT

y


Shamsuzzoha and Skogestad method with F=1 (overshoot=0.610)Proposed method with F=1 (overshoot=0.106)




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5 1

se

g

s

First-order unstable process


Not in training set

0 20 40 60 800

0.5

1

1.5

2

time

OUTPUT

y




Proposed method with F=1(overshoot=0.30)Proposed method with F=1(overshoot=0.607)


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6. Conclusion

From P-control setpoint experiment obtain:

1. Controller gain Kc0

2. Overshoot = (yp-y)/y3. Time to reach peak (overshoot), tp4. Steady state change, b= y/ys,

Estimate: y= 0.45(yp+ yu)

PID-tunings for the proposed Method:

py

pt

y sy

t0t

uy

sy

y

c c0K = K A ,F 2A= 1.55(overshoot) - 2.159(overshoot) + 1.35

I p pb

=min 0.645A t , 2.44t1-b

F

F=1:Good trade-off between performance and robustnessF>1:SmootherF


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References strm, K. J., Hgglund, T. (1984). Automatic tuning of simple regulators with specifications on phase and

amplitude margins,Automatica, (20), 645651. Desborough, L. D., Miller, R. M. (2002). Increasing customer value of industrial control performance

monitoringHoneywells experience. Chemical Process ControlVI (Tuscon, Arizona, Jan. 2001), AIChESymposium Series No. 326. Volume 98, USA.

Kano, M., Ogawa, M. (2009). The state of art in advanced process control in Japan, IFAC symposiumADCHEM 2009, Istanbul, Turkey.

Rivera, D. E., Morari, M., Skogestad, S. (1986). Internal model control. 4. PID controller design, Ind. Eng.Chem. Res., 25 (1) 252265.

Seborg, D. E., Edgar, T. F., Mellichamp, D. A., (2004). Process Dynamics and Control, 2nd ed., John Wiley& Sons, New York, U.S.A.

Shamsuzzoha, M., Skogestad. S. (2010). Report on the setpoint overshoot method (extended version)http://www.nt.ntnu.no/users/skoge/.

Skogestad, S., (2003). Simple analytic rules for model reduction and PID controller tuning, Journal ofProcess Control, 13, 291309.

Tyreus, B.D., Luyben, W.L. (1992). Tuning PI controllers for integrator/dead time processes,Ind. Eng. Chem.

Res. 26282631. Yuwana, M., Seborg, D. E., (1982). A new method for on-line controller tuning,AIChEJournal 28 (3) 434-440.

Ziegler, J. G., Nichols, N. B. (1942). Optimum settings for automatic controllers. Trans.ASME, 64, 759-768. Shamsuzzoha, M., Skogestad, S., (2010). The setpoint overshoot method: A simple and fast closed-loop

approch for PI tuning,Journal of Process Control 20 (2010) 12201234.


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Abstract

The PI/PID controller is widely used in the process industries due to simplicity androbustness, It has wide ranges of applicability in the regulatory control layer.

The proposed method is similar to the Ziegler-Nichols (1942) tuning method.

It is faster to use and does not require the system to approach instability withsustained oscillations.

The proposed tuning method, originally derived for first-order with delay processesand tested on a wide range of other processes and the results are comparable withthe Setpoint Overshoot Method and SIMC tunings using the open-loop model.

Based on simulations for a range of first-order with delay processes, simplecorrelations have been derived to give PI/PID controller settings similar to those ofthe Setpoint Overshoot Method tuning rules.

The detuning factor F that allows the user to adjust the final closed-loop responsetime and robustness.

The proposed method is the simplest and easiest approach for PID controllertuning available and should be well suited for use in process industries.


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Acknowledgement:

The author would like to acknowledge the support(Project Number:SB101016) provided by the Deanshipof Scientific Research at King Fahd University of

Petroleum and Minerals (KFUPM), Kingdom of SaudiArabia.

shamsuzzoha_mepec 2011 conference

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